Question

The ratio of the maximum deflections of a beam simply supported at its ends with an isolated central load and that of with a uniformly distributed load over its entire length, is

• A. 1
• B. 3/4
• C. 8/5
• D. 2/3

Hint:

- UDL causes less deflection compared to a concentrated load.

Answer 1

The Correct Option is C

Step 1: Finding deflection formulas. - Maximum deflection for point load at center: \[ \delta_{{point}} = \frac{PL^3}{48EI} \] - Maximum deflection for UDL over entire span: \[ \delta_{{UDL}} = \frac{5wL^4}{384EI} \] Step 2: Taking the ratio. \[ \frac{\delta_{{point}}}{\delta_{{UDL}}} = \frac{8}{5} \] Step 3: Selecting the correct option. Since the ratio is 8/5, the correct answer is (C).